The Income Expenditure Model

Income determination

Open economy Identity

$$GNP⟹C+I+G+(X-M)=Y=C+S+T+R_f\text{\hspace{1em}(1)}$$

Closed Economy Identity

$$C+I+G=Y=C+S+T\text{\hspace{1em}(2)}$$

Implicit Price Deflator

$$c+i+g=y=c+s+t\text{\hspace{1em}(3)}$$

Savings-Investments Balance¹

1. We can subtract the real consumption from each side of $(3)$:

$$y-c=\underbrace{i+g}\text{and}y-c=\underbrace{s+t}\text{\hspace{1em}(4)}$$

2. By moving $g$ term to the right hand side of equation $(4)$, we obtain another saving, investment balance.

$$\begin{array}{rl}i& =s+(t-g)\\ i& =s\end{array}\text{\hspace{1em}(5)}$$ $$\begin{array}{l}\begin{array}{rl}c+i+g& =c+s+t\\ i+g& =s+t\\ i& =s\end{array}\end{array}\}\text{Equilibrium Income}$$

$\overline{i}=i$

Investment

$i$ = Real investment; $I$ = Nominal investment

$$i\to \{\begin{array}{l}\text{Planned investment}\overline{i}\\ \text{Realised investment}i\end{array}$$

Example

Company A investing $10000cr$ in 2024-25 planned at 2024.

• Planned investment on 2024-25 $\to$ Feb 2024 $\overline{i}=10000cr$
• Accumulated inventory is $25\%$ (say) $\Delta inv=2500cr$
• Investments realized $i=75000cr$

If inventory accumulation $\Delta inv>0$ then $i<\overline{i}$, realized investments are lesser than what was planned.

Vice-versa, there will be inventory shortage and so our realized investments will have to be more than what was planned, i.e. $i>\overline{i}⟸\Delta inv<0$ .

$$i=\overline{i}+\Delta inv$$

• $\Delta inv$ is the unintended because of the unexpected changes in the income level
• which means unintended investment is the unforeseen changes in the inventories
  • $\Delta inv>0$: unintended accumulation of inventory
  • $\Delta inv<0$: unintended shortage of inventory

Thus, replacing the investment component in equation $(4)$,

$$\overline{i}+\Delta inv+g=s+t\text{\hspace{1em}(7)}$$ $$c+\overline{i}+\Delta inv+g=c+s+t\text{\hspace{1em}(8)}$$

Hence, $\Delta inv$ is now the balancing item in $(8)$.

Tax, consumption and savings

Tax is a function of income.

$$\begin{array}{rl}t=t(y)& ;t^{\prime }>0\\ c=c(y-t(y))& ;c^{\prime }>0\\ s=s(y-t(y))& ;s^{\prime }>0\end{array}$$

$t$, $c$ and $s$ depend on income. As income increases, all the 3 components $t$, $c$ and $s$ also increase.

Footnotes

1. S-I balance ↩